Is there no solution to the Euler Seven Bridges problem? Please list the reasons.

Along the border between Russia and Poland, there is a long Buge River that runs through the ancient Russian city of Konigsberg, which is today's northwest border city of Kaliningrad.

The Bug River runs through the city of Konigsberg. It has two tributaries, one is called the new river, and the other is called the old river. After they meet in the city center, they become a mainstream, called a big river. Between the old and new rivers and the big river, there is an island area, which is the bustling area of the city. The city is divided into four areas: North, East, South and Island, and there are seven bridges between the four areas.

People have lived on rivers and islands for a long time and shuttled between seven bridges. Some people ask: can you visit seven bridges at a time, and each bridge is only allowed to pass once? Many people are interested in this problem and have tried it one after another, but for a long time, it has never been solved. Finally, people had to throw this problem to Euler, an academician of the Russian Academy of Sciences, and ask him to help solve it.

In A.D. 1737, Euler received the "Seven Bridges Problem". At that time, he was thirty. Try it first, he thought. He started from the central island area, went to the north area through the 1 bridge, returned to the island area from the No.2 bridge, went to the east area through the No.4 bridge, went to the south area through the No.5 bridge, and then returned to the island area through the No.6 bridge. Now, only the No.3 and No.7 bridges have not been crossed.

Island northeast island south island north

This way of walking still doesn't work, because Bridge 5 hasn't crossed yet.

Euler can't even try a few tricks. This question is really not simple! He calculated that there were many moves, including * * *.

7×6×5×4×3×2× 1=5040 (species)

Boy, if you keep trying this method and this method, when will you get the answer? He thought, you can't keep trying like this, you have to think of other ways.

Clever Euler finally came up with a clever way. He used A to represent the island area, B, C, D, C and D to represent the north, east and west respectively, and the seven bridges were represented by arcs or straight lines. In this way, the problem of "Seven Bridges" becomes one of several branches of "Graph Theory", that is, whether the graph above can be drawn without repeating a stroke.

Euler concentrated on studying this figure and found that at every point in the middle, there was always a line drawn to that point and another line drawn from that point. That is, except the starting point and the ending point, the line passing through the middle point must be even. Like the picture above, because it is a closed curve, the lines passing through all points must be even. In this picture, there are five lines passing through point A, and these five lines pass through point B, and none of them are even, which means that no matter from that point, there is always a line that has not been drawn, that is, a bridge has not arrived. Euler finally proved that it is impossible to walk seven bridges at a time without repeating them.

The talented Euler summed up 5040 different moves with only one step of proof, which shows the power of mathematics! /view/ 142962.htm